[Druid] Why is +hit good for DPS?
 

(If this belongs in the Feral Druid DPS thread, please merge. Posting separately because of the difficulty I've had trying to follow specific theory discussions in the mixed advice/theorycraft mega-threads, but it might be just me.)

It's pretty well established that one of the best uses of item budget in PVE for rogues and cats is Hit Rating, at least up til the point where special attacks aren't missing (currently thought to be 8.6% vs bosses).

I'm working on a yet-another feral spreadsheet and the first cut showed 1 hit rating valued at 0.95AP. The gear set I used wasn't hit capped (according to the model I used) and all the other stats appeared about right. I couldn't find any obvious bug and back-of-the-envelope calculations seemed to confirm it. Either something's wrong with my assumptions, or my model, or +hit is much worse than I thought. Here's my rough calculation.

Assumptions

• I'm going to treat dodges/parries as misses, as the mechanics don't seem to differ for our purposes. Dodges/parries can't be removed by +hit of course, but I'm looking at the marginal value of hit when not hit-capped, so this doesn't matter.
• I'm going to ignore cooldowns on abilities and assume you're limited by energy rather than cooldowns. If you're missing so much that your energy bar fills up faster than you can use it, your DPS is going to suck, but this doesn't happen. More realistically, if a druid misses a mangle then it messes up their cycle. (A naive approximation of this effect - reducing mangle-uptime-on-rip by an additional 0.35% per %hit increased Hit Rating's worth to 1.13AP)

White damage
White damage is simple, it crits, hits, glances, or misses. Hit rating converts misses into hits.
Your average swing is weapondmg * (2*critrate + hitrate + g * glancerate). I'm not sure on the coefficient for glances but let's say 0.8. With 30% crit, 15% glance, 55% hit, 10% miss/dodge/parry, this is weapondmg * 1.27.
If your weapon damage is X, then 1%hit increases your average swing by 0.01X, which is 0.8% of your white damage.

Yellow damage
When you miss a special, or it gets dodged or parried, approximately 82% of the energy is returned. That is, the miss cost 18% of the energy of the attack. On average it'll take you 1/(1-miss) swings to land the attack, of which 1 costs full energy E and the rest cost 0.18E each. Average energy cost is F
That is, 0.22% reduction in cost per 1% reduction in misses.
(Less math approximation: missing increases your energy cost by 20%, missing 1% less reduces your energy cost by 0.2%)
Since your yellow DPS is cooldown limited, a 0.22% energy saving per 1% hit means 0.22% yellow DPS increase.

Tying it together
This depends on how much of your damage is yellow and how much is white. According to the cycle i modeled I had 39% white, 61% yellow (34% shred, 20% rip, 7% mangle).
Total damage increase from 1% hit: 0.39 * 100.8% + 0.61 * 100.22% = 100.45%
That is, 0.45% damage increase.

I'm not going to run through the full math for other stats, but 1% crit increases 80% of my damage (no rip) by a bit over 1%, and increases my combo point generation and thus yellow damage by about 0.7%, for around a 1.25% damage increase, around twice as good per rating point. Agility and Strength are even better of course, my sheet puts them at about 3 times as good as hit rating point-for-point.

What am I missing?

I didn't study your model completely through since im limited on time at the moment, but it seems that you are treating missed finishing moves as missed special/combo point moves. Missed finishing moves always return 0 energy, and you get absolutely no compensation for that. This means that +hit is very valuable for using Rip, and for Ferocious Bite its also more valueable because hitrating is usually cheaper than getting critchance either through agility or critrating.

Have you taken this into consideration?

I didn't realise that was the case, thanks! That's a decent effect, but still far from the whole discrepancy.
This is as you would expect - 1% hit goes from a 0.2% to a 1% decrease in rip energy cost, rip is 1/6 of cycle energy, so it's a 0.13%ish increase in yellow dps, 0.08%ish of overall dps.

I was also allowing OOC to proc on a miss, fixing this was another 0.02% total DPS.

Possibly it's just a bunch of these tiny errors. I expected a 'big' reason hit was good, rather than a bunch of little interactions with talents.

I wanted ot remind you on proccing OOC on missed attacks wasn't possible, but i got an error page when trying to edit my former post.

Personally i don't care much abotu +hit for the reason that it normally automatically comes on DPS gear. I am personally a tank and sometimes healer, i rarely DPS, but for the few random DPS pieces of gear i have gathered i have 8.3% hit. It usually comes automatically with the rest of the stats. Once i get Illhoof staff i will be over the +hit cap and well need to cut somewhere eventually.

Edit: Also in addition to OOC procs, +hit also helps items like Dragonspine Trophy or Romulo's Poison Vial which are all decent Feral Druid DPS items.

It's not that +Hit by itself is such an amazing stat, it's that it makes all of your other ones better.

Lets say you have no +Hit and miss exactly 8.64% of the time--8.6 for the sake of this argument. Let's also say that you have the potential to do 1000 DPS, just to keep numbers nice and round. Due to misses, you are reducing your damage output by 86 DPS, without considering the combo-point, energy, and global cooldown mechanics. 'Losing' a GCD to a miss, without considering the lost damage or energy, costs you output by wasting a second of time. Considering that warlocks are modeling this effect so exactly on their spreadsheets, finding that the lost GCDs involved in recasting CoA reduce their dps below what is possible with a CoD + Shadowbolts during the extra GCDs, this effect on Druid & Rogue DPS must also be nontrivial. So, you easily lose 10% of your potential damage output by ignoring +Hit.

Furthermore, as Athinira pointed out, missing results in less procs. Simply put, this means you get less Omen of Clarity procs, discounting the ability to proc anything else. From everything I've been able to find, there appears to be a disagreement over whether OOC is a 1 PPM or 2 PPM proc--assuming worst case, we have a 1/60 (1.667%) chance, per hit, to proc OOC and we should be making ~1.25 attacks per second or 5 attacks in 4 seconds. Thus, every 4 seconds, there is about an 8% chance that Omen of Clarity will have procced. If we miss 8.6% of the time, there is a 36% chance that we have missed one of those swings! This results in a, reduced, expected procrate of 5.1% per 5 attacks (I think; I may be projecting with projections, which could be a statistical no-no but I'm fairly sure I'm on solid ground).

This isn't even covering lost combo points / energy due to misses, nor am I even considering dodge at this point; however, a raw 10% reduction in potential DPS, not including procs, and a 36% reduction in expected OOC procs is a pretty hefty penalty in my book.

Lost GCDs for melee classes are a lot less meaningful than for casters, since there's no requirement to be constantly casting. That isn't the difference.

I agree with pretty much all of this. That said, item budget wise Hit is definately not the best stat available at least from a lot of spreadsheets I've seen. Since hit rating, crit rating (and any other combat ratings), Str and Agi all cost the same in an item budget, the order (once you've reached high enough AP) would be:

Agi>Str>AP>Crit Rating>Haste Rating>Hit rating>FCS

The other effect of +hit is that it means you can manage energy cycles much better. If you can always make sure you mangle with 81+ energy (or rip->mangle with 70+) then you can get the most effect out of it. It you miss this attack even once, it can cause a missed partial/full energy tick, which is a lot of DPS.

Other than that, losing GCD's isn't an issue for druids (or rogue really), because of the energy regeneration system and that GCD is only one second rather than one and a half. Making a generalisation that it isn't an issue for melee classes isn't entirely true - warriors can be limited in certain situations by GCD's too.

The effect of +hit is certainly noticeable. I have ~6.6% hit in my current DPS gear; I still notice strings of 2-3 shred misses in a row, and the effect of missed finishing moves is pretty major, not to mention the procs missed from 2t4 or OoC.

The other benefit of +hit is that it comes in addition to other stats. The system for itemisation means that the more stats you have ilvl points spread over, the more stat points total you get (in very simple terms). Picking up items without hit on is a waste of the extra points you can get by stat-spreading.

I'm also amazed that you seem to have haste rating as worth more than hit rating, I was always under the impression that haste rating is one of the worst stats for druids (going by my own % of white damage compared to yellow).

Modeling yellow damage is very hard, but I tried to find a relationship for white damage and came up with this chart. When you factor in OOC, and energy loss from misses I think we can put this argument to bed and say hit is king.

While what you said about hit having low effect on specials is totally true, remember the rating cost of 1 hit, bumping it back up to a far less than useless stat. Remember that while 1% crit is clearly more DPS than 1% hit for the reasons stated in the first post, it also costs significantly more rating. I've done some rough numbers in the past and got that 1 crit rating is not too far off from 1 hit rating - and to actually tell which is better you'll have to run a lot more accurate numbers/models that include all components of your DPS (and then compare to str/AP too).

The problems with your chart are:
-As you already probably understand, hit rating is a huge increase for white damage regardless. But white damage is far far from the majority of your DPS.
-You make it based on AP, while the real "DPS function" is a multiple variable function and includes your current hit and crit as well. With that graph (if it's correct) you pretty much had to assume a certain amount of starting crit and hit.

Also since DPS is a multiple variable function and to tell how much it increases when you increase each of its variables, you can assume that dDPS/d(stat) hardly changes when you only swap one item and make an approximation that:
newDPS-oldDPS = crit*dDPS/dCrit+AP*dDPS/dAP+hit*dDPS/dAP.
Then recalculate (or better, have excel recalculate) the dDPS/d(stat) whenever your gear actually changes significanly enough to affect those values. You'll notice you need quite a few gear upgrades before those get changed by a little (which can also be somewhat seen on the graph above).

Yep; believe my sheet somewhat reflects this as well, modeling shred and mangle misses simply as % reduction on damage, but it magnifies the effect that you demonstrated since more damage is being affected.

Since the chart is white damage only, it more illustrates that hit is NOT the best stat available.

White damage is about 35-40% of your total damage. The rest being yellow. For yellow damage static AP increases are more valuable due to the multipliers in all the special attacks. Further, crit is WAY more valuable due to Primal Fury. Also with a white attack a miss removes 100% of the dps of that attack. For yellow attacks it only removes a portion (17% i believe) due to the fact that special attacks are energy limited for the most part.

To further illustrate this, consider white attacks (that cannot glance for simplicity). Here 1% hit and 1% crit (neglecting the crit increase talent) give the same increase in DPS assuming you are not hit capped, i.e., 1 crit and 1 miss is the same damage as 2 hits. In this situation it it clear that hit rating is better since it only takes 15.8 hit rating for 1% whereas it takes 22.1 crit rating for 1%. However in the yellow damage situation, 1 crit and 1 miss is superior to 2 hits. Assuming mangle, the 1 crit 1 miss scenario costs 48 energy, whereas the 2 hits scenario costs 80 energy, both giving the same damage. Including predatory instincts and primal fury it is clear that crit is FAR superior to hit when yellow damage is included (and thus so is Agi, even moreso since it adds 1 AP in addition to a similar amount of crit as 1 crit rating).

Actually it's more like 31-35% these days...

Indeed; however, missing on a yellow attack costs you time and energy. Worst case, we're talking 2 seconds because you missed down to below the cost of an ability immediately after a tick.

Simplifying in that manner actually hurts the valuation of +Hit as, without glances, the average hit is always going to be the same damage as the next hit; with glances, the average hit that lands is lower and adding more +Hit actually ~raises~ your average hit more than one would expect (you're going from, say 60% Hits / 25% glances / 15% Avoid to 68.6% Hit / 25% Glance / 7.4% Avoid).

With regard to the yellow attacks, I really couldn't tell you which is really better. On paper, it looks like Crit/Agi are simply the way to go for them but it all depends on how much the additional AP/Crit helps your white/yellow attacks in relation to how much +Hit helps. It's a big picture kinda thing -- if +Hit helps your white just enough, and yellow barely at all, it still could very well be 'better'.

Seriously, play around with the spreadsheet and see what happens; if it says "Crit is better than Hit at 0% Hit" then it's probably correct unless I screwed up how I model one or the other. Admittedly, hit is more valuable than the sheet models due to the fact that a yellow miss results in a CP/Energy loss (not to mention I never modeled a miss chance into rip), but it's fairly on target and should give you a decent idea of what is better/worse. Just remember to trust the values for the custom entries more than the other ones as they actually model stuff like Primal Fury properly (everything includes Pred. Instincts).

Glances or no glances, the effect of 1% hit and 1% crit for white damage is EXACTLY the same. The ratings are different though.
For yellow 1% crit is greatly superior to 1% hit and costs somewhat more.
When you add it up together, they come close enough for you to not be able to tell the difference between 1 hit rating and 1 crit rating without making at least a half-decent spreadsheet and calculating it taking everything into account.

For white damage, 1 hit is always superior as long as you can still benefit from it -- two hits, vs 1 crit / 1 miss, yields twice the chance for a proc.